Aaron, Nithin2025-09-182025-09-182025-09-182025-09-18https://hdl.handle.net/10012/22474The primary focus of this thesis is on developing the normal-mode sampling algorithm, an importance sampling method specifically designed for path-integral quantum Monte Carlo simulations of flexible molecular systems. This work is motivated by the desire to include vibrational degrees of freedom in numerical studies of confined molecular lattices. Describing the dynamics of a molecular system using its normal modes naturally allows for the inclusion of molecular rotations, translations, and even vibrations. We first introduce a novel density matrix factorization that arises from decomposing our system Hamiltonian into its harmonic and anharmonic terms. The normal-mode sampling algorithm is then constructed using this factorization. We also integrate Jacobi coordinates with our normal-mode sampling algorithm to allow for separability between translational and ro-vibrational degrees of freedom. Finally, we validate our normal-mode sampling algorithm in the context of path-integral quantum Monte Carlo simulations of several flexible molecular systems, namely the water monomer, dimer, hexamer cage, and hexamer prism. For each of these systems, we calculate the ground-state energy and various structural properties, benchmarking our results against exact diagonalization, path integral molecular dynamics, and diffusion Monte Carlo studies from the literature.enquantum Monte Carlopath integral ground statenormal-mode samplingJacobi coordinatesmolecular flexibilitywater clustersMaster Thesis